Remove the carpet from the stairs, if any, by walking to the top step and prying the staples or nails from the uppermost edge using a pry bar. If needed, cut through the carpet using a utility knife to make access easier. Pull the carpet off all the way down to the bottom stair and discard it.
Insert a tape measure under the lip of one of the existing stair treads to determine how far out it extends from the riser. Note the measurement.
Remove the existing stair treads with the pry bar and needle-nose pliers. You may need to hammer up from under the lip of the tread first, then follow up with the pry bar and pliers, removing all of the fasteners holding the treads on. Always pull out the fasteners at the same angle in which they're attached so they come out straight.
Sweep the stairs from top to bottom to remove all wood, dust and dirt particles.
Measure the width -- wall stringer to wall stringer -- and depth -- riser to riser -- of the first step with the measuring tape. Add the length of the lip that you measured earlier to the latter measurement. Mark these measurements on the new unfinished oak stair tread with the pencil and straightedge.
Wear protective goggles and cut the new stair tread along the pencil lines you drew previously using a table saw or circular saw.
Test the fit of the new stair tread by placing it into position. Make any adjustsment needed. Apply construction adhesive to unfinished oak stair tread.
Insert a finishing nail into the oak treads at each of the four corners using a nail gun.
Repeat the process of measuring and cutting on each remaining step and stair tread.
Wait until the construction adhesive dries completely, then apply wood stain in the desired color to the oak stair treads using a foam paint brush.